That mom needs to prioritize that child. This is the unfolding of issues that point to this kid being destined for a ruined life. She's asking you to stay, but I don't hear where she's saying she's making a plan to address this. This would be like your kid running a high fever, and you don't think you need to head for the pediatrician's office.

Number 1, she needs to call and make an appointment with her pediatrician. The child's doctor should then refer her to a child behavioral expert. And she needs to not delude herself that this is something that can principally be addressed with medication . . . which is what mothers nowadays often want to believe. I don't think it's just a coincidence that there is no father in this home. Depending on her resources, she may need to enroll this boy into a program for very maladjusted children. Here's a short article: Violent Behavior in Children and Adolescents

Here's another relevant article: Violent Behavior in Children and Adolescents

For you to stick around absorbing abuse from this child would be you enabling a bad situation, so jettison the guilt. The mother is in over her head with this and does not know how to effectively parent this child. It is probably indicated that this child attend a facility on a day basis, or as a resident. I've worked in child psychiatric treatment facilities. The kids are there for one reason: they are dangerous. Kids as young as five are treated in these places. Some go home every afternoon. Some are there round the clock. These are kids who could not be managed by their parents, or in "treatment foster care" because they are just too violent. Yes, as young as five. I didn't stay in this line of work long. It's extremely challenging. Working with adult inmates in prison is easier. But staff who do stay with this kind of work include some very gifted people and it does take very specialized training. Expecting you to deal with this behavior is ridiculous. The mother can't even deal with it. She needs major help from trained professionals.